Create frac_test.cpp

Author: juan-c-s

code/math/__Test/frac_test.cpp

@@ -0,0 +1,74 @@
+// https://algo.sk/br24/problem.php?problem=d2-avgavg
+#include <bits/stdc++.h>
+
+#define forn(i,n) for(int i=0; i < n; ++i)
+#define for1(i,n) for(int i=1; i <= n; ++i)
+#define fore(i,l,r) for(int i=l; i <= r; ++i)
+#define el '\n'
+#define sz(v) int(v.size())
+#define all(v) v.begin(),v.end()
+#define d(x) cout <<#x << " : " << x << el;
+
+using namespace std;
+
+typedef long long ll;
+typedef vector<int> vi;
+typedef vector<ll> vll;
+
+struct frac{
+  ll num, den;
+  frac(){}
+  frac(ll num, ll den):num(num), den(den){ 
+    if(!num) den = 1;
+    if(num > 0 && den < 0) num = -num,  den = -den;
+    simplify(); 
+  }
+  void simplify(){
+    ll g = __gcd(abs(num), abs(den));
+    if(g) num /= g,  den /= g;
+  }
+  frac operator+(const frac& b){ return {num*b.den + b.num*den, den*b.den};}
+  frac operator-(const frac& b){ return {num*b.den - b.num*den, den*b.den};}
+  frac operator*(const frac& b){ return {num*b.num, den*b.den};}
+  bool operator<(const frac& b)const{ return num*b.den < den*b.num; }
+};
+
+int main(){
+  ios_base::sync_with_stdio(0);
+  cin.tie(0); cout.tie(0);
+  int n, k, a[34], sum;
+  bool dp[34][34][34][101][101];
+  cin >>n >> k;
+  forn(i, n) cin >> a[i], sum += a[i];
+
+  queue<array<int, 5>> q;
+  auto go = [&](int i, int s1, int s2, int sum1, int sum2){
+    if(!dp[i][s1][s2][sum1][sum2]) q.push({i, s1, s2, sum1, sum2});
+    dp[i][s1][s2][sum1][sum2] = 1;
+  };
+  pair<double, frac> best = {1e9, frac{1, 1}};
+  frac me = frac(k, 1);
+  // Caso base
+  go(0, 0, 0, 0, 0);
+  while(sz(q)){
+    auto [i, s1, s2, sum1, sum2] = q.front(); q.pop();
+    // Condicion de parada
+    if(i == n){
+      int s3 = n - s1 - s2;
+      if(!s1 || !s2 || ! s3) continue;
+      int sum3 = sum - sum1 - sum2;
+      frac a = frac{sum1, s1}, b = frac{sum2, s2}, c = frac{sum3, s3};
+      frac avg = (a + b + c) * frac{1, 3};
+      frac dif = avg - me;
+      double cur = abs(1.0*dif.num / dif.den);
+      best = min(best, {cur, avg});
+      continue;
+    }
+    // Transiciones
+    go(i+1, s1+1, s2, sum1 + a[i], sum2);
+    go(i+1, s1, s2+1, sum1, sum2 + a[i]);
+    go(i+1, s1, s2, sum1, sum2);
+  }
+  auto [_, avg] = best;
+  cout << avg.num << "/" << avg.den << el;
+}